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Yo, fellow autodidact, Catching down from episode 30 backwards. NZ math professor NJ Wildberger says no. He is a finitist. You can only use Greek methods and per Hippasus; the square root of two is rejected because it isn't a proper rational number of two integers, it is an essential infinite decimal. All infinitistic results are rejected because of the irrationality of the equality two different infinities that have the same Cantor cardinality (aka even two real line segments that have a metric and have a different length). Goedel's diagonal argument is rejected for the same reason. I won't be commenting on older episodes in general.

Amazing, hats off! I have enjoyed Gravitation by M-T-W since i was a HS student when it first came out in 1973. Covers the physics up to that point. Not so good on the math IMHO.

I spent a whole month considering the nuanced terminology in Differential Geometry. For example, are the terms "fundamental" and "form" used appropriately? "Fundamental" clearly applies to the First Fundamental Form (which describes the intrinsic geometry of a surface) and the Second Fundamental Form (which describes the extrinsic geometry), as these are truly foundational to the geometry of surfaces. However, it is less fitting for the Third Fundamental Form, which serves more as a complement to the first two. The term "form" is consistently used throughout, reflecting their bilinear nature. I struggle to get consistency in Differential Geometry books in languages other than English. 😉

I wasn’t expecting Žižek (wow, those z's with *strešica* - what a fancy name for the caron diacritic!) on a Möbius Strip alongside Kant, Lacan, Marx, and Hegel. Interestingly, I think of Žižek through the lens of another prominent Slovenian figure: Melania Trump (yes, I’m borrowing Žižek’s irony here). Žižek’s Lacanian critique of ideology often explores how nationalism and cultural identity are commodified. He avoids simplistic political rhetoric, and offers a nuanced analysis of how individuals and nations construct ideological fantasies to sustain their sense of identity. He also critiques how late-stage capitalism transforms even resistance into a product. In contrast, Melania’s rise to First Lady can be seen as a commodified identity, a spectacle of the global capitalism Žižek often critiques. Her carefully curated public persona can be interpreted as an ideological construction. From Žižek’s perspective, Melania's branding of identity aligns with the fantasies that sustain contemporary ideological frameworks.

I'm not sure why you want to undertake this read-out-loud exercise - perhaps this has been a successful teaching experiment for you? BUT, I mainly wanted to say, as a physicist, I did in fact use Kreyszig as my first book on DG. I found it very approachable and inspired me (along with the lovingly illustrated volume, "Gravitation" by Misner, Thorne and Wheeler) to select courses on especially on GR while a physics undergrad. It was this funny coincidence that brought me here. Hope that was of some use.

I hope you are doing well at the beginning of 2025. I spent the end of 2024 moving and reorganizing my new house, which was quite a big task but also rewarding. <3

Oh yeah RUclips recommendation algorithm, we're getting to the real spicy stuff now.

Amazing !!

fire

You get a 👍 for the opening alone

This rocks, I will listen to this every time doing analysis now

Did not think the start would be that... he's spitting..

Hell yeah

0:38 bro was breaking it down 😭

looking dapper man

I think a better place to understand GR is (Wald book considered tops. Lee is standard text as noted) For the Grad intro cannot beat Schuller 100th Anniversary of GR ruclips.net/p/PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_ for Basic Start that gets all the way is the XylyXylyX What is a Series What is a Tensor ( skips to What is a Manifold , half way) ruclips.net/p/PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c Ending with What is GR ruclips.net/p/PLRlVmXqzHjURQIIebhT7UNTwGQHUEPlsb

That opening though ❤

ts got me osculating

FIre at the begining!

when will the full song be on spotify... i need it to study differential geometry

Soooo good

32:44 There is a fundamental difference in how we approach geometry in 2D versus higher dimensions. In 2D, since any holomorphic function (all power series, exponential functions, trigonometric functions, and their compositions) is conformal, and any local conformal mapping can be approximated by Möbius transformations, there exists an infinite array of possible mappings. In higher dimensions (n ≥ 3), Liouville's theorem imposes a strict restriction, as only Möbius transformations can be conformal. *The key here is to understand that the limit of 5 inversions is not related to dimensionality, but rather comes from the algebraic structure of Möbius transformations.*

I genuinely enjoy your videos

I wish I had vitiligo.

Also, Daisuke Samejima is a Japanese artist who creates hyperrealistic paintings on spherical canvases. His manipulation of perspective, by compensating for distortions, is as a nice example of practical Differential Geometry. I absolutely love his work. His "flatballs," featuring photorealistic Japanese suburbia, remind me of the wormhole from Interstellar.

By the way, there is an award-winning, equal-area world map projection created by Hajime Narukawa, which maintains more accurate scaling of areas: the AuthaGraph minimizes distortion of land and ocean shapes through a polyhedral approach.

You're doing a fantastic job! Could you help me with something unrelated: I have a SafePal wallet with USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). How should I go about transferring them to Binance?

I need to point some things out here. 1) The original comment contained a mistake, the subgroups N and H are not supposed to be disjoint, but their intersection is supposed to be trivial, that is {e}. You correctly guessed what it means, but we still don't say that those subgroups are disjoint. 2) The modulo operation is related to modulo as an equivalence, but is not quite the same. We have that a and b are congruent mod n if and only if (a mod n) = (b mod n), their remainders from division by n are the same. I am pointing this out for educational purposes. 3) Your definition of G/H is wrong, its supposed to be the set {gH : g in G}, where gH = {gh : h in H}. The set G/H has sets of the form gH as elements. 4) I'm not sure what you're saying when you say that phi is injective. To prove that phi is injective, what you want to do is take x in G such that phi(x) = e. This e is a neutral element of (G/H) x (G/N), and not H (note that H is a subgroup of G, so this would clash with our already established notation). This means that xH = eH and xN = eN, or equivalently, that x is both in H and in N, so x = e. This is how the proof is supposed to go. 5) The group G and (G/N) x (G/H) are indeed not always isomorphic. An easy example would be to let H = N = {e} and G to be any finite group.

An example of how our current understanding of Fundamental Physics can be incomplete or inconsistent is the *Abraham-Minkowski controversy,* which revolves around the correct expression for the momentum of electromagnetic radiation in a medium. Specifically, Abraham's suggestion is that the momentum of light should increase as its velocity decreases when it passes through a material; this implies that light behaves like a classical object with mass. On the other hand, Minkowski's prediction is that the momentum of light remains constant regardless of its velocity in a material; this perspective is consistent with the behavior of a massless particle (a photon). In other words, *the controversy centers on how much of the momentum should be attributed to the material and how much to the electromagnetic field.* - This affects our comprehension of energy-momentum conservation. If Minkowski's perspective is correct, it could lead to the possibility of "reactionless" drives that produce motion without expelling a propellant. *This is Elon Musk's dream, of course.* However, a recent satellite testing program failed to deploy an experimental propulsion system (remember the frenzy surrounding EmDrive?) due to ongoing power-system issues.

I'm exploring Mike McCulloch's Quantized Inertia Theory in the hopes that it may hint at a higher framework for relativity and quantum theory. McCulloch suggests that inertia is not an inherent property of matter itself, but rather a result of the interactions between matter and the surrounding quantum vacuum. I'm not wearing a tin foil hat, though - I'm not expecting faster-than-light travel or even Jetson-esque flying cars.

Hey man, I was wondering, you ever thought about doing "deeper" videos? I really enjoy the problem-solving and all that, but what about something more fun, like a problem from group theory, galois, measure theory, etc. I'd really love to see how you go about that, I mean, to give an example problem from my last midterm: Let H and K be normal subgroups of G, where H and K are disjoint sets, show that G is isomorphic to to some subgroup of G/H x G/K. I can give a few more ideas, but tbf, my knowledge is somewhat limited T_T, but yah

There is no continuous bijection from (0, 1] to (0, 1]^2 by the way. The simplest argument I can come up with is as follows, using dimension theory: Write (0, 1] as countable union of compact intervals I_n, then the restriction of the map to I_n is a homeomorphism onto its image, so (0, 1]^2 is a countable union of closed 1-dimensional spaces. By the countable sum theorem, we obtain that (0, 1]^2 is 1-dimensional, contradiction. (here dimension means inductive or covering dimension, which are the same in this case)

You pronounce Banach wrong, the "ch" is pronounced like "h" (voiceless velar fricative). I think the word "house" in English has a pretty close "h" (voiceless glottal fricative). I hope this helps 🙂

Wow, this is ingenius and unique content so far. Great Loved it ❤

Thank You ❤❤❤

Wow, this is an interesting niche of youtube. All for it!

Your youtube videos are very good quality but your videos are not SEO so no views so your videos are not getting to your subscribers not ranking and your videos are not reaching viewers, videos need fast SEO once videos don't get viewers. I can work with you if you want

straight 1 hour of chill music for sleep. amazing will use it when im stressed

54:30 The Liouville surface seems to be related to the torus, which is also connected to the Hopf fibration. I'm wondering if the Liouville surface can be thought of as a type of Hopf fibration or something entirely different.

7:00 I used algorithms to create sets of five special dice that have six sides, numbered from 1 to 30, with numbers that are evenly distributed on each die and add up to 93. When you roll these dice against each other, the chances of one die rolling higher than the other two is about 55.5% (20/36 probability). The idea behind these special dice is similar to 'Rock-Paper-Scissors-Spock-Lizard'. I was hoping to use these dice sets as a tool for role-playing games or similar projects. Here is an example: Given the following 6-sided dice (and their sides as a list) - Die A {1,2,21,22,23,24}, Die B {3,4,16,17,26,27}, Die C {5,6,8,15,29,30}, Die D {7,10,11,18,19,28}, Die E{ 9,12,13,14,20,25} -, the probability that one die rolls higher ("beats") than other two is 20/36: A beats D and E; B beats A and E; C beats A and B; D beats B and C; E beats C and D. 😉

2:45 My native language is Brazilian Portuguese, but I've been studying and using English as my primary language for about 10 years now. As for my nickname, it's actually a funny story that happened by chance!

Is this for real?😆🤣😂🤣😆. Listen, I am a fully mathematically literate and competent engineer of 35 years experience. I’ve taught at university. But I cannot but think that this must be some kind of joke!

i love how scotty chen just got smoke the entire video🤣

im not even gonna lie my calculus isnt even that good so i dont understand any of this. im only liking the video beacuse of the ending🤣 28:03

Wow I have to follow a path of pure self-study. This is a wonderful resource and I very much appreciate you. Thank you so very much.

Great video!

I used this book back in college! I am glad the algorithm directed me here.

Yaksimaz Very nice, I like